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6 July, 14:58

The center of a hyperbola is (-2,4), and one vertex is (-2,7). The slope of one of the asymptotes is 1/2.

What is the equation of the hyperbola in standard form?

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  1. 6 July, 15:12
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    The equation of the hyperbola in standard form is (y^2 / 49) - (x^2 / 4) = 1.

    Step-by-step explanation:

    Hyperbola is a section of the cone formed by intersecting a right circular cone with a plane at an angle where both halves of the cone are intersected. The vertex and the center of the hyperbola are present both on the same line x = - 2. (i. e. on the y-axis), hence the branches of the hyperbola are above and below each other. The slope of the asymptotes is + (or) - a/b.

    Here the vertex is 7 units so a = 7 and a^2 = 49.

    Slope of the asymptotes = a/b = 1/2.

    Here b = 2 and b^2 = 4.

    The standard equation of the hyperbola is,

    (y^2 / 49) - (x^2 / 4) = 1.
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